The Stark shift of the hyperfine coupling constant is investigated for a P donor in Si far below the ionization regime in the presence of interfaces using tight-binding and band minima basis approaches and compared to the recent precision measurements. In contrast with previous effective mass-based results, the quadratic Stark coefficient obtained from both theories agrees closely with the experiments. It is also shown that there is a significant linear Stark effect for an impurity near the interface, whereas, far from the interface, the quadratic Stark effect dominates. This work represents the most sensitive and precise comparison between theory and experiment for single donor spin control. Such precise control of single donor spin states is required particularly in quantum computing applications of single donor electronics, which forms the driving motivation of this work.